package com.wc.AlgoOJ_homework.AlgoOJ_test4.I_最大的与运算;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * @Author congge
 * @Date 2024/3/15 20:52
 * @description http://43.138.190.70:8888/p/708?tid=65e5720827489dab814f4cab
 */
public class Main {
    static FastReader sc = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);
    static int N = 200010;
    static int[] a = new int[N];
    static int[] c = new int[31];
    static int t, n, k;

    public static void main(String[] args) {
        t = sc.nextInt();
        while (t-- > 0) {
            n = sc.nextInt();
            k = sc.nextInt();
            for (int i = 1; i <= n; i++) a[i] = sc.nextInt();
            for (int i = 1; i <= n; i++) {
                for (int j = 30; j >= 0; j--) {
                    c[j] += (a[i] >> j & 1);
                }
            }
            for (int i = 30; i >= 0; i--) {
                if (c[i] != n) {
                    if (n - c[i] <= k) {
                        k -= n - c[i];
                        c[i] = n;
                    }
                }
            }
            int res = 0;
            for (int i = 30; i >= 0; i--) {
                if (c[i] == n) {
                    res |= 1 << i;
                }
            }
            out.println(res);
            Arrays.fill(c, 0);
        }
        out.flush();
    }
}

class FastReader {
    StringTokenizer st;
    BufferedReader br;

    FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    String nextLine() {
        String s = "";
        try {
            s = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return s;
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    // 是否由下一个
    boolean hasNext() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                String line = br.readLine();
                if (line == null)
                    return false;
                st = new StringTokenizer(line);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return true;
    }
}
